Note, that the key feature of log function used here is not its slow growth, but the fact that it takes negative values on small inputs. For example, if we take the function u(r)=log (r+1), so that u(0)=0, then RC holds.
Although there are also solutions that prevent RC without taking negative values, e.g u(r) = exp{-1/r}.
Note, that the key feature of log function used here is not its slow growth, but the fact that it takes negative values on small inputs. For example, if we take the function u(r)=log (r+1), so that u(0)=0, then RC holds.
Although there are also solutions that prevent RC without taking negative values, e.g u(r) = exp{-1/r}.